Francesco Lin

Francesco Lin serves as an Associate Professor in the Department of Mathematics at Columbia University, with his office located in Room 613. He is actively engaged in research and teaching, with upcoming responsibilities including a topics course at the University of Pisa during Fall 2025 leave and Modern Analysis II in Spring 2026.

Lin's research centers on low-dimensional topology and geometric analysis, specializing in gauge theory, Floer homology, hyperbolic geometry, and spectral theory. His work critically examines the Dirac and Maxwell equations, exploring their implications for geometric structures and topological invariants in three and four-dimensional manifolds. This focus bridges analytical methods with deep topological questions.

Recent publications demonstrate a cohesive trajectory in applying spectral methods and Floer theory to hyperbolic manifolds. Key investigations include Dirac spectral flow, adjunction inequalities, integral rigidity in Seiberg-Witten theory, and the topology of Dirac equations on spectrally large manifolds. These works reveal consistent emphasis on three-manifold geometry, spectral invariants, and the interplay between gauge theory and hyperbolic structures.

His research program is supported by two National Science Foundation grants: "New directions in monopole Floer homology" (DMS-2203498) and "Monopole Floer homology and the torus of flat connections" (DMS-2503714). While no current advisees are documented, Lin maintains active teaching commitments and collaborates with researchers including M. Lipnowski, B. Martelli, and M. Miller Eismeier.